Almost Optimality of the Orthogonal Super Greedy Algorithm for μ-Coherent Dictionaries

被引：3

作者：

Shao, Chunfang ^{[1
]}

Chang, Jincai ^{[1
]}

Ye, Peixin ^{[2
,3
]}

Zhang, Wenhui ^{[2
,3
]}

Xing, Shuo ^{[2
,3
]}

机构：

[1] North China Univ Sci & Technol, Coll Sci, Tangshan 063210, Peoples R China

[2] Nankai Univ, Sch Math, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

AXIOMS | 2022年 / 11卷 / 05期

基金：

中国国家自然科学基金;

关键词：

orthogonal super greedy algorighm; coherence; best n-term approximation; Lebesgue-type inequality; MATCHING PURSUIT; SPARSE SOLUTION; APPROXIMATION; INEQUALITIES; RECOVERY;

D O I：

10.3390/axioms11050186

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the approximation capability of the orthogonal super greedy algorithm (OSGA) with respect to mu-coherent dictionaries in Hilbert spaces. We establish the Lebesgue-type inequalities for OSGA, which show that the OSGA provides an almost optimal approximation on the first [1/ (18 mu s)] steps. Moreover, we improve the asymptotic constant in the Lebesgue-type inequality of OGA obtained by Livshitz E D.

引用

页数：17

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